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[jabaws.git] / website / archive / binaries / mac / src / disembl / Tisean_3.0.1 / source_f / slatec / rfftb1.f

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+*DECK RFFTB1
+      SUBROUTINE RFFTB1 (N, C, CH, WA, IFAC)
+C***BEGIN PROLOGUE  RFFTB1
+C***PURPOSE  Compute the backward fast Fourier transform of a real
+C            coefficient array.
+C***LIBRARY   SLATEC (FFTPACK)
+C***CATEGORY  J1A1
+C***TYPE      SINGLE PRECISION (RFFTB1-S, CFFTB1-C)
+C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
+C***AUTHOR  Swarztrauber, P. N., (NCAR)
+C***DESCRIPTION
+C
+C   Subroutine RFFTB1 computes the real periodic sequence from its
+C   Fourier coefficients (Fourier synthesis).  The transform is defined
+C   below at output parameter C.
+C
+C   The arrays WA and IFAC which are used by subroutine RFFTB1 must be
+C   initialized by calling subroutine RFFTI1.
+C
+C   Input Arguments
+C
+C   N       the length of the array R to be transformed.  The method
+C           is most efficient when N is a product of small primes.
+C           N may change so long as different work arrays are provided.
+C
+C   C       a real array of length N which contains the sequence
+C           to be transformed.
+C
+C   CH      a real work array of length at least N.
+C
+C   WA      a real work array which must be dimensioned at least N.
+C
+C   IFAC    an integer work array which must be dimensioned at least 15.
+C
+C           The WA and IFAC arrays must be initialized by calling
+C           subroutine RFFTI1, and different WA and IFAC arrays must be
+C           used for each different value of N.  This initialization
+C           does not have to be repeated so long as N remains unchanged.
+C           Thus subsequent transforms can be obtained faster than the
+C           first.  The same WA and IFAC arrays can be used by RFFTF1
+C           and RFFTB1.
+C
+C   Output Argument
+C
+C   C       For N even and for I = 1,...,N
+C
+C                C(I) = C(1)+(-1)**(I-1)*C(N)
+C
+C                     plus the sum from K=2 to K=N/2 of
+C
+C                      2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
+C
+C                     -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
+C
+C           For N odd and for I = 1,...,N
+C
+C                C(I) = C(1) plus the sum from K=2 to K=(N+1)/2 of
+C
+C                     2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
+C
+C                    -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
+C
+C   Notes:  This transform is unnormalized since a call of RFFTF1
+C           followed by a call of RFFTB1 will multiply the input
+C           sequence by N.
+C
+C           WA and IFAC contain initialization calculations which must
+C           not be destroyed between calls of subroutine RFFTF1 or
+C           RFFTB1.
+C
+C***REFERENCES  P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
+C                 Computations (G. Rodrigue, ed.), Academic Press,
+C                 1982, pp. 51-83.
+C***ROUTINES CALLED  RADB2, RADB3, RADB4, RADB5, RADBG
+C***REVISION HISTORY  (YYMMDD)
+C   790601  DATE WRITTEN
+C   830401  Modified to use SLATEC library source file format.
+C   860115  Modified by Ron Boisvert to adhere to Fortran 77 by
+C           changing dummy array size declarations (1) to (*).
+C   881128  Modified by Dick Valent to meet prologue standards.
+C   891214  Prologue converted to Version 4.0 format.  (BAB)
+C   900131  Routine changed from subsidiary to user-callable.  (WRB)
+C   920501  Reformatted the REFERENCES section.  (WRB)
+C***END PROLOGUE  RFFTB1
+      DIMENSION CH(*), C(*), WA(*), IFAC(*)
+C***FIRST EXECUTABLE STATEMENT  RFFTB1
+      NF = IFAC(2)
+      NA = 0
+      L1 = 1
+      IW = 1
+      DO 116 K1=1,NF
+         IP = IFAC(K1+2)
+         L2 = IP*L1
+         IDO = N/L2
+         IDL1 = IDO*L1
+         IF (IP .NE. 4) GO TO 103
+         IX2 = IW+IDO
+         IX3 = IX2+IDO
+         IF (NA .NE. 0) GO TO 101
+         CALL RADB4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
+         GO TO 102
+  101    CALL RADB4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
+  102    NA = 1-NA
+         GO TO 115
+  103    IF (IP .NE. 2) GO TO 106
+         IF (NA .NE. 0) GO TO 104
+         CALL RADB2 (IDO,L1,C,CH,WA(IW))
+         GO TO 105
+  104    CALL RADB2 (IDO,L1,CH,C,WA(IW))
+  105    NA = 1-NA
+         GO TO 115
+  106    IF (IP .NE. 3) GO TO 109
+         IX2 = IW+IDO
+         IF (NA .NE. 0) GO TO 107
+         CALL RADB3 (IDO,L1,C,CH,WA(IW),WA(IX2))
+         GO TO 108
+  107    CALL RADB3 (IDO,L1,CH,C,WA(IW),WA(IX2))
+  108    NA = 1-NA
+         GO TO 115
+  109    IF (IP .NE. 5) GO TO 112
+         IX2 = IW+IDO
+         IX3 = IX2+IDO
+         IX4 = IX3+IDO
+         IF (NA .NE. 0) GO TO 110
+         CALL RADB5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+         GO TO 111
+  110    CALL RADB5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+  111    NA = 1-NA
+         GO TO 115
+  112    IF (NA .NE. 0) GO TO 113
+         CALL RADBG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
+         GO TO 114
+  113    CALL RADBG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
+  114    IF (IDO .EQ. 1) NA = 1-NA
+  115    L1 = L2
+         IW = IW+(IP-1)*IDO
+  116 CONTINUE
+      IF (NA .EQ. 0) RETURN
+      DO 117 I=1,N
+         C(I) = CH(I)
+  117 CONTINUE
+      RETURN
+      END